Estimating project cash flows and taxes

A capital budgeting decision is only as good as the cash flow forecast behind it. The decision rules of lesson 7 tell us to discount a project's cash flows, but which cash flows? This lesson sets out the principles for identifying the cash flows that belong in the analysis, shows how to build a project's free cash flows year by year, and explains how taxes, especially the tax deductions for capital spending, change the result. The tax rules differ sharply between Canada and the United States, so this lesson uses each country's system on its own site. Nothing here is tax advice; rules change often, and real projects need current rules and professional advice.

Incremental cash flows

The cash flows that matter are incremental: the difference between the firm's cash flows if it takes the project and its cash flows if it does not. Every item in the analysis should pass that test. Several common traps follow from it. Sunk costs, money already spent and unrecoverable whatever the decision, are irrelevant: a market study paid for last year should not count against the project. Opportunity costs are relevant: if the project uses land the firm already owns, the cash the firm could get by selling or renting that land is a cost of the project, even though no cheque is written. Side effects matter: a new product that takes sales from an existing one (cannibalization) should be charged with the lost profit, while one that boosts sales of other products should be credited with the gain. Allocated overhead counts only to the extent that the project actually increases it.

Financing costs are excluded from project cash flows. Interest, debt repayments and dividends are payments to investors, and the required return of those investors is captured in the discount rate, the weighted average cost of capital developed in lesson 11. Subtracting interest from the cash flows and also discounting at a rate that includes the cost of debt would count it twice. Finally, be consistent about inflation, as lesson 3 explained: if revenues and costs are forecast in nominal dollars that include expected price increases, discount at a nominal rate.

The parts of a project's cash flows

A project's free cash flow in each year has three parts, matching the free cash flow definition of lesson 2. The first is after-tax operating cash flow: incremental revenue minus incremental cash operating costs, minus the taxes on that difference. The second is the tax saving from deducting the cost of the capital assets over time, called the depreciation tax shield, or in Canada the capital cost allowance tax shield. The third is investment: the capital spending at the start (and any later), the investment in net working capital, and their recovery at the end through the after-tax salvage value of the assets and the release of the working capital.

Here \( D_t \) is the tax deduction for the capital asset in year \( t \) and \( T \) the marginal tax rate. The term \( T \cdot D_t \) shows that depreciation itself is not a cash flow, but its effect on taxes is: each dollar deducted saves \( T \) dollars of tax. Working capital is usually invested at the start or as sales grow and recovered at the end of the project, when inventory is sold off and receivables are collected; ignoring it overstates the NPV of almost any project, because it moves cash from early years to late years.

Tax deductions for capital spending

In Canada, the tax deduction for depreciable property is the capital cost allowance (CCA). Assets are grouped into classes, each with a prescribed rate, and most classes use the declining balance method: each year the deduction is the class rate times the remaining undepreciated capital cost (UCC). For example, Class 8 (most machinery and equipment not in another class) has a rate of 20 %, Class 10 (vehicles) 30 %, Class 50 (general computer equipment) 55 %, and Class 1 (most buildings) 4 %. Normally the half-year rule allows only half the usual deduction in the year of acquisition. Budget 2024 and the Fall Economic Statement 2024 proposed, and Budget 2025 extended, a set of measures that Parliament enacted in March 2026: an accelerated first-year allowance for most property acquired from 2025 and available for use before 2030 (the deduction in the first year is about one and a half times the normal full-year rate, with the half-year rule suspended), phasing down for 2030 to 2033; and immediate 100 % expensing, the productivity super-deduction, for manufacturing and processing equipment (Class 53), clean energy equipment and zero-emission vehicles available for use before 2030, plus productivity-enhancing assets such as computer equipment and patents. Because the deduction continues on the declining balance indefinitely, Canadian analysts value the whole stream with a closed-form formula rather than year by year.

In the formula, \( C \) is the capital cost, \( d \) the CCA rate, \( T \) the tax rate and \( r \) the discount rate. With the accelerated first-year allowance, the factor \( (1 + 0.5r) \) becomes \( (1 + 1.5r) \); with immediate expensing, the shield is simply \( CT/(1+r) \) if the deduction is claimed at the end of the first year. When an asset is sold, its proceeds (up to the original cost) are deducted from the UCC of the class, so the firm loses the future CCA on that amount. As long as the class remains open, the present value of the lost shield is \( S\,d\,T/(d+r) \) discounted from the date of sale, where \( S \) is the salvage value. If the class is closed, a terminal loss or recapture arises instead.

A complete project analysis

Bringing the pieces together, consider a project that requires equipment costing $800,000, has a five-year life, and will be sold for $150,000 at the end. It needs $60,000 of extra working capital at the start, recovered at the end. It is expected to increase revenue by $500,000 a year and cash operating costs by $230,000 a year. The discount rate is 10 %. The tax treatment of the equipment follows each country's rules.

# Project NPV with capital cost allowance (Class 8, 20 %, accelerated first year)
cost, salvage, nwc, years = 800_000, 150_000, 60_000, 5
revenue, op_costs, tax, r, d = 500_000, 230_000, 0.265, 0.10, 0.20
after_tax_operating = (revenue - op_costs) * (1 - tax)
pv_ops = sum(after_tax_operating / (1 + r) ** t for t in range(1, years + 1))
# CCA tax shield: first-year deduction of 1.5 x d, then d on the declining balance
pv_shield = cost * d * tax / (d + r) * (1 + 1.5 * r) / (1 + r)
pv_lost_shield = salvage * d * tax / (d + r) / (1 + r) ** years
pv_salvage = salvage / (1 + r) ** years
pv_nwc = -nwc + nwc / (1 + r) ** years
npv = -cost + pv_ops + pv_shield - pv_lost_shield + pv_salvage + pv_nwc
for label, v in [("after-tax operating", pv_ops), ("CCA tax shield", pv_shield), ("lost shield on salvage", -pv_lost_shield),
                 ("salvage", pv_salvage), ("working capital", pv_nwc), ("equipment", -cost)]:
    print(f"{label:24s} {v:12,.0f}")
print(f"{'NPV':24s} {npv:12,.0f}")
# With immediate expensing (for example Class 53 manufacturing equipment under the 2025 measures)
pv_shield_100 = cost * tax / (1 + r)
print(f"NPV if the full cost were deductible in year 1: {npv - pv_shield + pv_shield_100:,.0f} (ignoring the salvage adjustment)")

after-tax operating           752,282
CCA tax shield                147,758
lost shield on salvage        -16,454
salvage                        93,138
working capital               -22,745
equipment                    -800,000
NPV                           153,978
NPV if the full cost were deductible in year 1: 198,948 (ignoring the salvage adjustment)

Replacement decisions

Many capital budgeting decisions are about replacing an existing asset with a new one. The incremental cash flows are then the differences: the cost of the new machine minus the after-tax proceeds from selling the old one, the change in operating costs, the change in tax deductions, and the difference in salvage values at the end. The old machine's original cost is sunk; what matters is what it could be sold for now and what keeping it would cost in the future.

Practical forecasting

Forecasts of revenue and costs are where most capital budgeting errors begin. Managers proposing a project tend to be optimistic, and they often have an incentive to be. Good practice includes checking forecasts against the experience of past projects, asking why the firm has an advantage that will let it earn more than its cost of capital, building forecasts from specific assumptions (market size, share, price, unit costs) rather than from a target NPV, and reviewing projects after they are completed. Lesson 9 shows how sensitivity, scenario and simulation analysis expose the assumptions that matter most. And whatever the tax rules, the project should make economic sense before the tax shield: an investment that is worthwhile only because of a tax incentive is vulnerable if the rules change.